Question

If $\sqrt{18225}=135,$ then the value of $(\sqrt{182.25}+\sqrt{1.8225}+\sqrt{0.018225}+\sqrt{0.00018225})$ is:

• A. 1.49985
• B. 14.9985
• C. 149.985
• D. 1499.85

Answer 1

The correct option is B 14.9985

$\sqrt{18225}=135$ (Given)

$\therefore$ $\sqrt{182.25}=\sqrt{\frac{18225}{100}}=\frac{\sqrt{18225}}{\sqrt{100}}=\frac{135}{10}=13.5$

$\sqrt{18225}=\sqrt{\frac{18225}{10000}}=\frac{\sqrt{18225}}{\sqrt{10000}}=\frac{135}{100}=1.35$

$\sqrt{0.018225}=\sqrt{\frac{18225}{1000000}}=\frac{\sqrt{18225}}{\sqrt{1000000}}=\frac{135}{1000}=0.135$

$\sqrt{0.00018225}=\sqrt{\frac{18225}{100000000}}=\frac{\sqrt{18225}}{\sqrt{100000000}}=\frac{135}{10000}=0.0135$

$\therefore$ $\sqrt{182.25}+\sqrt{1.8255}+\sqrt{0.018225}+\sqrt{0.00018225}$

$=13.5+1.35+0.135+0.0135$

$=14.9985$

$\therefore$ Correct answer : Option B.